Thin-film circuit modules are commonly used in space-constrained applications, such as hearing instrument or cell phone products. In some thin-film circuit modules, perovskite or pyrochlore materials, such as (Ba1-xSrx)TiO3 (hereinafter BST), are used as high K capacitor dielectrics. The high dielectric constant (high-K) of these materials allows for significant miniaturization of these devices. Many capacitors can also be fabricated on a single substrate along with other passive electronic components (integrated passive component chips) to form part of electronic devices such as cell phone power amplifier modules, GPS receivers, etc.
These high-K dielectrics, such as BST, are also tunable, i.e. the dielectric constant of the is varied by changing the applied electric field. Tunable capacitors rely on the variable dielectric properties of the high-K dielectric. The capacitance at zero bias is a maximum and the capacitance drops with applied voltage. The change in capacitance allows these units to be used to create tunable circuits in filters, matching networks, resonant circuits and other applications from audio to RF and microwave frequencies. The dielectric constant of the tunable dielectric material determines the capacitance as C=A/d, where  is the dielectric constant of the tunable material, A is the area of the electrodes and d is the separation of the electrodes and thickness of the tunable material. A DC voltage is applied to the electrodes to induce an electric field in the tunable dielectric. The ∈ of the tunable dielectric material is a function of the electric field, E=V/d, and thus the capacitance is a function of voltage.
Ferroelectric materials are also electrostrictive. As an electric field is applied, which lowers the dielectric constant, the piezoelectric constant of the material becomes non-zero. As a result, the electric field causes a physical change of the lattice constants of the film. Application of an AC signal to the piezoelectric material causes acoustic vibrations of atoms in the crystalline lattice, which is called electromechanical coupling. Therefore, any AC signal on the tunable capacitor under bias produces an acoustic response. At certain frequencies, the acoustic response of the structure will be resonant and some of the AC signal power will be converted into acoustic vibrations causing a loss of signal amplitude. The effect is seen as a narrow band of frequencies where the Q-factor of the capacitor is very low.
It has been shown that acoustic resonance can be at least partially cancelled by a multilayer capacitor that has two capacitors, one with a positive DC bias and one with a negative DC bias. It was previously thought that the number of layers of positively DC-biased dielectrics had to be equal to the number of negatively DC-biased dielectrics in order to observe the acoustic resonance cancellation effect. This was based on the theory that acoustic vibrations from the positively biased capacitors would interfere with the opposite phase acoustic vibrations of the negatively biased capacitors. These earlier efforts are fairly limited in operable frequency range. For instance, FIG. 1 shows a simulated Q factor vs. frequency within the operable frequency range for a two-layer capacitor (solid line) 1.